Optical metrology techniques generally referred to as scatterometry offer the potential to characterize parameters of a workpiece (i.e., a sample) during a manufacturing process. In practice, light is directed onto a periodic grating formed in a workpiece and spectra of reflected light are measured and analyzed to characterize the grating. Characterization parameters may include critical dimensions (CDs), sidewall angles (SWAs) and heights (HTs) of gratings, material dispersion parameters, etc., which affect the polarization and intensity of the light reflected from or transmitted through a material. Characterization of the grating may thereby characterize the workpiece as well as manufacturing process employed in the formation of the grating and the workpiece. For example, the optical metrology system 100 depicted in FIG. 1 can be used to determine the profile of a grating 102 formed on a semiconductor wafer 104. The grating 102 can be formed in test areas on the wafer 104, such as adjacent to a device formed on the wafer 104. The optical metrology system 100 can include a photometric device with a source 106 and a detector 112. The grating 102 is illuminated by an incident beam 108 from source 106. In the present exemplary embodiment, the incident beam 108 is directed onto the grating 102 at an angle of incidence θi with respect to normal of the grating 102 and an azimuth angle φ (e.g., the angle between the plane of incidence beam 108 and the direction of the periodicity of the grating 102). A diffracted beam 110 leaves at an angle of θd with respect to normal and is received by the detector 112. The detector 112 converts the diffracted beam 110 into a measured metrology signal. To determine the profile of the grating 102, the optical metrology system 100 includes a processing module 114 configured to receive the measured metrology signal and analyze the measured metrology signal.
Analysis of measured spectra generally involves comparing the measured sample spectra to simulated spectra 116 to deduce a scatterometry model's parameter values that best describe the measured sample. As used herein, “model” refers to a scatterometry model and “parameter” refers to a model parameter of the scatterometry model unless otherwise specified.
FIG. 2 illustrates a method 200 for analyzing a diffracting structure in accordance with one embodiment of the invention. At block 202, an optical metrology system (e.g., the optical metrology system 100 of FIG. 1) performs measurements of a sample with a diffracting structure. Performing measurements involves shining light on the sample and measuring spectral information for the sample such as reflectance. At block 204, the optical metrology system identifies an initial model of the measurement process. Identifying the initial model of the measurement process includes constructing a geometric model of the diffracting structure, determining how to parameterize the geometric model, characterizing the incident light, and characterizing the optical measurement system. Typically, model parameters include layer thicknesses, material dispersion parameters, SWAs and HTs, angle of incidence of light directed onto the diffracting structure, calibration parameters of an optical measurement system, etc. Based on the model parameters, the optical metrology system determines reflectance from the diffracting structure (e.g., via a simulation). Reflectance is generally determined using rigorous diffraction modeling algorithms, such as the Rigorous Coupled Wave Analysis (RCWA) method based on Maxwell's equations.
At block 206, the optical metrology system attempts to fit the modeled data obtained at block 204 to the experimental data obtained at block 202. Fitting the modeled data generally involves comparing the modeled data to the experimental data and determining an error between the two sets of data. The initial model identified is generally based on expected parameters of the diffracting structure, and typically results in an error significant enough to require additional iterations of blocks 204 and 206. Therefore, the optical metrology system performs a regression analysis. In the regression analysis, the optical metrology system determines the next set of model parameters to use, 208. The next set of model parameters is generally based on the derivative of the error. The optical metrology system repeats blocks 204 and 206 until one or more conditions occur indicating the regression should be terminated. Conditions can include reaching (or sufficiently approaching) convergence such that the error is below a threshold value. Other conditions that can terminate the regression include: reaching a maximum number of iterations, determining that the difference between previous model parameters and current model parameters is less than a threshold value, and/or any other conditions justifying discontinuing further iterations of block 204 and 206.
Once a condition is reached for terminating the regression, the optical metrology system can determine values of parameters of the actual diffracting structure based on the best fit model parameters, at block 210. Upon completing the regression, the scatterometry model is typically close enough to the actual diffracting structure that determining values of some parameters of the actual diffracting structure may simply involve ascertaining the best fit model parameters. This can be true, for example, for geometric parameters that have a one-to-one correspondence with a single parameter used in the scatterometry model. Determining other parameters of the actual diffracting structure may involve additional operations such as adding two parameters of the scatterometry model together.
The method 200 involves computations which can be time intensive and resource intensive (e.g., requiring large amounts of computer memory and/or processing power). For example, computing spectral information for a model at block 204 and determining next parameters at 208 generally involve complex derivatives. Furthermore, scatterometry computations have become increasingly complex due to, for example, increasing complexity of the geometry of the diffracting structures being evaluated. Complex geometry can make computations such as the derivatives used at blocks 204 and 208 infeasible or impractical. Computations which are time and resource intensive can inhibit the method 200 from providing measurements in a sufficiently timely manner for use in some applications such as semiconductor manufacturing.